| Spline Toolbox Release Notes | |
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Version 3.3 (R2006a) Spline Toolbox™ Software
This table summarizes what's new in Version 3.3 (R2006a):
| New Features and Changes |
Version Compatibility Considerations |
Fixed Bugs and Known Problems |
Related Documentation at Web Site |
| Yes Details below |
Yes--Details labeled as Compatibility Considerations, below. See also Summary. |
Bug Reports |
No |
New features and changes introduced in this version are
Controlled Extrapolation Beyond the Basic Interval
When a spline in ppform is evaluated at some site outside its basic interval, the value at that site of the 'nearest' polynomial piece is returned. On the other hand, when a spline in B-form is evaluated outside its basic interval, the value 0 is returned. These are the two extreme ways of extrapolating a spline beyond its basic interval. Assuming the spline to be of order k, we use, in the first case, a polynomial of order k that matches k-fold the spline at the relevant endpoint of its basic interval, and this we call extrapolation of order k. In the second case, we use a polynomial of order 0 (i.e., the zero polynomial) that matches the spline 0-fold (i.e., perhaps not at all) at the relevant endpoint of its basic interval, and this we call extrapolation of order 0.
The new toolbox function, fnxtr(f,j), returns a spline in ppform that extrapolates the spline in f to order j, with 2 the default value for j in case j is not explicitly given. This new feature is of immediate use for the evaluation of smoothing splines since, by its definition, a smoothing spline of order 2m is to be extrapolated beyond its basic interval to order m, not 0 nor 2m.
A new example, Least-Squares Approximation by "Natural" Cubic Splines in the Spline Toolbox documentation makes essential use of this new feature.
For more information, see the fnxtr reference page.
Interpolating Planar Tangent-Continuous Piecewise Biarc Curve
The new toolbox function, rscvn(p,u), provides the planar tangent-continuous piecewise biarc curve that passes, in order, through the given points p(:,1), p(:,2), ..., p(:,n) in the plane and, for all j, is, at the point p(:,j), perpendicular to the vector u(:,j). Default values for the vectors u(:,j) are used when the user does not supply them.
rscvn makes use of the fact that Spline Toolbox can handle rational splines, hence can represent exactly curves made up of circular arcs. The particular rational spline used here is piecewise quadratic, with two pieces between neighboring data points, hence the term biarc. Because of the geometry of the construction used, users need not provide parameter values associated with the given data points, as they would have to if they wanted to use csapi or spapi for the construction of a smooth interpolating curve.
An added example, in the Spline Toolbox demo "More Spline Curves", illustrates what may have been a very early use of a tangent-continuous piecewise circular arc curve.
For more information, see the rscvn reference page.
rsmak Now Provides a Torus As Well As a Longer Arc
rsmak now provides the rBform of a torus for which you can specify the radii of the outer and the inner circle (of which it is, in a way, the tensor product). Precisely,
returns a description of the torus centered at the origin and with the z-axis its axis whose major circle has the specified radius, and whose minor circle has the radius radius*ratio.
returns the circular arc, of the given radius and the given center, that starts at angle alpha and ends at angle beta. If the difference between alpha and beta is (in absolute value) greater than 2*pi, the arc includes a full circle.
rsmak Input and Output For Getting an Arc Is Changed
Getting an arc of specified extent used to require the following command:
in which the beginning angle, alpha, and end angle, beta, for the arc are specified by two separate input arguments. These two arguments are now combined into one 2-vector argument, as follows:
Further, the arc now produced starts at angle alpha and ends at angle beta and may well cover an entire circle and even more than one. Formerly, the arc produced would never exceed a half circle.
Compatibility Consideration
You are encouraged to change to the new rsmak syntax. The earlier syntax, which required separate arguments for alpha and beta, continues to be valid but may be removed in a future release.
Part 'k...' For a Ppform Disallowed
The request fnbrk(f,part), for the part 'k...' of a ppform now produces an error message.
Compatibility Consideration
The request fnbrk(f,part), with part a string starting with 'k', used to return the order of the spline in f in case the spline is in ppform, while it returns the knot sequence of that spline in case the spline is in B-form. As this can lead to confusion when a user forgets whether the spline of interest is in ppform or B-form, and the former response was undocumented anyway, asking for the part 'k...' of a ppform now produces an error message.
Strange Error Message from fnval Eliminated
Specifying the evaluation sites for fnval as a column cell array does not automatically result in an error message.
Compatibility Consideration
When the evaluation sites for fnval are specified by a column cell array rather than the required row cell array, a mysterious error message would result. In this situation, fnval now tries to make sense of the input by changing the column cell array to a row cell array and give an error message only if the length of the resulting row cell array is incompatible with the number of variables for the function being evaluated.
Changes to Spline Tool
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| Version 3.3.1 (R2006b) Spline Toolbox™ Software | Version 3.2.2 (R14SP3) Spline Toolbox™ Software | |
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